There is simple cipher that translates number to series of . ( )
In order to encrypt a number (0 .. 2147483647) to this representation, I (think I) need:
0 . 6 (()()) 1 () 7 (...()) 2 (()) 8 ((.())) 3 (.()) 9 (.(())) 4 ((())) 10 (().()) 5 (..()) 11 (....()) 227 (................................................()) 2147483648 ((..........()))
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.IO;
static class P
{
static List<int> _list = new List<int>();
public static int Nth(int n)
{
if (_list.Count == 0 || _list.Count < n)
Primes().Take(n + 1);
return _list[n];
}
public static int PrimeOrd(int prime)
{
if (_list.Count == 0 || _list.Last() < prime)
Primes().First(p => p >= prime);
return (_list.Contains(prime)) ? _list.FindIndex(p => p == prime) : -1;
}
public static List<int> Factor(int N)
{
List<int> ret = new List<int>();
for (int i = 2; i ≤ N; i++)
while (N % i == 0)
{
N /= i;
ret.Add(i);
}
return ret;
}
public static IEnumerable<int> Primes()
{
_list = new List<int>();
_list.Add(2);
yield return 2;
Func<int, bool> IsPrime = n => _list.TakeWhile(p => p ≤ (int)Math.Sqrt(n)).FirstOrDefault(p => n % p == 0) == 0;
for (int i = 3; i < Int32.MaxValue; i += 2)
{
if (IsPrime(i))
{
_list.Add(i);
yield return i;
}
}
}
public static string Convert(int n)
{
if (n == 0) return ".";
if (n == 1) return "()";
StringBuilder sb = new StringBuilder();
var p = Factor(n);
var max = PrimeOrd(p.Last());
for (int i = 0; i ≤ max; i++)
{
var power = p.FindAll((x) => x == Nth(i)).Count;
sb.Append(Convert(power));
}
return "(" + sb.ToString() + ")";
}
}
class Program
{
static void Main(string[] args)
{
string line = Console.ReadLine();
try
{
int num = int.Parse(line);
Console.WriteLine("{0}: '{1}'", num, P.Convert(num));
}
catch
{
Console.WriteLine("You didn't entered number!");
}
}
}
The problem is SLOWNESS of procedure PrimeOrd. Do you know some FASTER solution for finding out order of prime in primes?
P.S. The biggest prime less than 2,147,483,648 is 2,147,483,647 and it's 105,097,565th prime. There is no need to expect bigger number than 2^31.
You should cache the primes to _list and then use it for both Factor and PrimeOrd. Additionally avoid operators LINQ operators like TakeWhile that create values that you throw away.
Here's an optimized version:
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
static class P
{
private static List<int> _list = new List<int>();
public static int Nth(int n)
{
if (_list.Count == 0 || _list.Count <= n)
{
GenerateNextPrimes().First(p => _list.Count >= n);
}
return _list[n];
}
public static int PrimeOrd(int prime)
{
var primes = GrowPrimesTo(prime);
return primes.IndexOf(prime);
}
public static List<int> Factor(int N)
{
List<int> ret = new List<int>();
GrowPrimesTo(N);
for (int ixDivisor = 0; ixDivisor < _list.Count; ixDivisor++)
{
int currentDivisor = _list[ixDivisor];
while (N % currentDivisor == 0)
{
N /= currentDivisor;
ret.Add(currentDivisor);
}
if (N <= 1)
{
break;
}
}
return ret;
}
private static List<int> GrowPrimesTo(int max)
{
if (_list.LastOrDefault() >= max)
{
return _list;
}
GenerateNextPrimes().First(prime => prime >= max);
return _list;
}
private static IEnumerable<int> GenerateNextPrimes()
{
if (_list.Count == 0)
{
_list.Add(2);
yield return 2;
}
Func<int, bool> IsPrime =
n =>
{
// cache upperBound
int upperBound = (int)Math.Sqrt(n);
for (int ixPrime = 0; ixPrime < _list.Count; ixPrime++)
{
int currentDivisor = _list[ixPrime];
if (currentDivisor > upperBound)
{
return true;
}
if ((n % currentDivisor) == 0)
{
return false;
}
}
return true;
};
// Always start on next odd number
int startNum = _list.Count == 1 ? 3 : _list[_list.Count - 1] + 2;
for (int i = startNum; i < Int32.MaxValue; i += 2)
{
if (IsPrime(i))
{
_list.Add(i);
yield return i;
}
}
}
public static string Convert(int n)
{
if (n == 0) return ".";
if (n == 1) return "()";
StringBuilder sb = new StringBuilder();
var p = Factor(n);
var max = PrimeOrd(p.Last());
for (int i = 0; i <= max; i++)
{
var power = p.FindAll(x => x == Nth(i)).Count;
sb.Append(Convert(power));
}
return "(" + sb.ToString() + ")";
}
}
class Program
{
static void Main(string[] args)
{
string line = Console.ReadLine();
int num;
if(int.TryParse(line, out num))
{
Console.WriteLine("{0}: '{1}'", num, P.Convert(num));
}
else
{
Console.WriteLine("You didn't entered number!");
}
}
}